TESTING/LIN/clavhe.f(3)

💅 TESTING/LIN/clavhe.f(3) 💅

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🌸 NAME 🌸

TESTING/LIN/clavhe.f

🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

subroutine clavhe (uplo, trans, diag, n, nrhs, a, lda, ipiv, b, ldb,
    info)
    CLAVHE

👑 Function/Subroutine Documentation 👑

subroutine clavhe (character uplo, character trans, character diag, integer
    n, integer nrhs, complex, dimension( lda, * ) a, integer lda, integer,
    dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb,
    integer info)
    CLAVHE

🎀 Purpose 🎀

Okay so here’s the vibe: CLAVHE performs one of the matrix-vector operations

x := A*x  or  x := A^H*x,

where x is an N element vector and A is one of the factors from the block U*D*U' or L*D*L' factorization computed by CHETRF. 🫶

If TRANS = 'N', it multiplies by U or U * D (or L or L * D).

If TRANS = 'C', it multiplies by U' or D * U' (or L' or D * L'). slay. 💅

💖 Parameters 💖

• UPLO — UPLO is CHARACTER*1. Specifies whether the factor stored in A is upper or lower triangular.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• TRANS — TRANS is CHARACTER*1. Specifies the operation to be performed:
  • = 'N': x := A*x
  • = 'C': x := A^H*x
• DIAG — DIAG is CHARACTER*1. Specifies whether or not the diagonal blocks are unit matrices. If the diagonal blocks are assumed to be unit, then A = U or A = L, otherwise A = U*D or A = L*D.
  • = 'U': Diagonal blocks are assumed to be unit matrices.
  • = 'N': Diagonal blocks are assumed to be non-unit matrices.
• N — N is INTEGER. The number of rows and columns of the matrix A. N >= 0. ✨
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of vectors x to be multiplied by A. NRHS >= 0. 💖
• A — A is COMPLEX array, dimension (LDA,N). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CHETRF_ROOK. Stored as a 2-D triangular matrix. 🦋
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N). 🌟
• IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D, as determined by CHETRF.
  • If UPLO = 'U':
    • If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. (If IPIV( k ) = k, no interchange was done).
    • If IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged, D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
  • If UPLO = 'L':
    • If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. (If IPIV( k ) = k, no interchange was done).
    • If IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged, D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
• B — B is COMPLEX array, dimension (LDB,NRHS). On entry, B contains NRHS vectors of length N. On exit, B is overwritten with the product A * B. 🔥
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N). 🌈
• INFO — INFO is INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -k, the k-th argument had an illegal value

🌈 Author 🌈

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 151 of file clavhe.f. 🫶

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. ✨

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